Congratulations to Mike. He joins 31 other current and retired members of the department who are FRS.
Mike says, with the help of ChatGPT (humorous version): "Delighted to be elected a Fellow of the Royal Society. I plan to celebrate in the traditional scientific way: mild astonishment, followed by tea."
Stipendary Lectureship in Probability and Statistics at Trinity College
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Image: interior of Trinity College Chapel. If you haven't made a tour of college chapels in Oxford, do, because it is well worth making.
Bestvina--Brady groups were first introduced by Bestvina and Brady for their interesting finiteness properties. In this talk, we discuss their Dehn functions, that are a notion of isoperimetric inequality for finitely presented groups and can be thought of as a "quantitative version" of finite presentability. A result of Dison shows that the Dehn function of a Bestvina--Brady group is always bounded above by a quartic polynomial.
Our main result is to compute the Dehn function for all finitely presented Bestvina--Brady groups. In particular, we show that the Dehn function of a Bestvina--Brady group grows as a polynomial of integer degree, and we present the combinatorial criteria on the graph that determine whether the Dehn functions of the associated Bestvina--Brady group is linear, quadratic, cubic, or quartic.
This is joint work with Chang and García-Mejía.